111 (number)

111 is a natural number that comes after 110 and before 112. It is an odd number, as it cannot be divided by two. In general mathematics, it belongs to the three-digit numbers in the base-10 system.

The most notable property of 111 is that it is a composite number: 111 = 3 × 37. Its divisors are therefore 1, 3, 37, and 111. The sum of its digits — 1+1+1 = 3 — shows that it is divisible by three, which is the standard test for divisibility by three.

Mathematical properties

111 is a repunit — a number consisting of the digit 1 repeated — when written in base 10. It equals 1 + 10 + 100. Other repunits of the same kind are 11, 1111, and 11111. The third repunit in base 10 is not a prime number, as it is divisible by 3 and 37.

Additionally, when 37 is multiplied by 3, 6, 9, and similar multiples, the result is 111, 222, 333, and so on in the same pattern where all digits are identical. This occurs because 111 = 3 × 37, so 37 × 3n produces a three-digit number with all digits the same.

Representation in other bases

When written in the binary system, 111 becomes 1101111. It is important to distinguish: the binary string "111" represents seven (4+2+1), whereas "111" in base 10 represents one hundred eleven. This distinction is often discussed when teaching number base systems.

Public use

Many countries use 111 as a telephone number for particular services, such as emergency calls in some regions. It also appears in games, historical records, and general counting. This public use has no particular mathematical relationship to the properties of the number.